Finite Math Examples

$3500 = 1000 e^{0.04 x}$

Step 1

Rewrite the equation as $1000 e^{0.04 x} = 3500$ .

$1000 e^{0.04 x} = 3500$

Step 2

Divide each term in $1000 e^{0.04 x} = 3500$ by $1000$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $1000 e^{0.04 x} = 3500$ by $1000$ .

$\frac{1000 e^{0.04 x}}{1000} = \frac{3500}{1000}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $1000$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{1000 e^{0.04 x}}{1000} = \frac{3500}{1000}$

Step 2.2.1.2

Divide $e^{0.04 x}$ by $1$ .

$e^{0.04 x} = \frac{3500}{1000}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Cancel the common factor of $3500$ and $1000$ .

Tap for more steps...

Step 2.3.1.1

Factor $500$ out of $3500$ .

$e^{0.04 x} = \frac{500 (7)}{1000}$

Step 2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.2.1

Factor $500$ out of $1000$ .

$e^{0.04 x} = \frac{500 \cdot 7}{500 \cdot 2}$

Step 2.3.1.2.2

Cancel the common factor.

$e^{0.04 x} = \frac{500 \cdot 7}{500 \cdot 2}$

Step 2.3.1.2.3

Rewrite the expression.

$e^{0.04 x} = \frac{7}{2}$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{0.04 x}) = \ln (\frac{7}{2})$

Step 4

Expand the left side.

Tap for more steps...

Step 4.1

Expand $\ln (e^{0.04 x})$ by moving $0.04 x$ outside the logarithm.

$0.04 x \ln (e) = \ln (\frac{7}{2})$

Step 4.2

The natural logarithm of $e$ is $1$ .

$0.04 x \cdot 1 = \ln (\frac{7}{2})$

Step 4.3

Multiply $0.04$ by $1$ .

$0.04 x = \ln (\frac{7}{2})$

Step 5

Divide each term in $0.04 x = \ln (\frac{7}{2})$ by $0.04$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $0.04 x = \ln (\frac{7}{2})$ by $0.04$ .

$\frac{0.04 x}{0.04} = \frac{\ln (\frac{7}{2})}{0.04}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $0.04$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{0.04 x}{0.04} = \frac{\ln (\frac{7}{2})}{0.04}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{7}{2})}{0.04}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (\frac{7}{2})}{0.04}$

Step 5.3.2

Divide $7$ by $2$ .

$x = \frac{\log_{2.71828182} (3.5)}{0.04}$

Step 5.3.3

Log base $2.71828182$ of $3.5$ is approximately $1.25276296$ .

$x = \frac{1.25276296}{0.04}$

Step 5.3.4

Divide $1.25276296$ by $0.04$ .

$x = 31.31907421$